Abstract
The two-phase macroscopic kinetic model of the end of a microtubule is extended to microtubules in solution, with two free ends. The theoretical treatment of this system is complicated by the possibility of microtubules shortening all the way to disappearance. Another possibility, if a microtubule is shortening from one end only (and has a GTP cap on the other end), is that completed shortening will leave a residual cap from which growth can then take place at both ends. Two approximations are introduced.
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